Problem: Solve for $x$ and $y$ using substitution. ${-6x+4y = 2}$ ${x = -y-7}$
Answer: Since $x$ has already been solved for, substitute $-y-7$ for $x$ in the first equation. ${-6}{(-y-7)}{+ 4y = 2}$ Simplify and solve for $y$ $6y+42 + 4y = 2$ $10y+42 = 2$ $10y+42{-42} = 2{-42}$ $10y = -40$ $\dfrac{10y}{{10}} = \dfrac{-40}{{10}}$ ${y = -4}$ Now that you know ${y = -4}$ , plug it back into $\thinspace {x = -y-7}\thinspace$ to find $x$ ${x = -}{(-4)}{ - 7}$ $x = 4 - 7$ ${x = -3}$ You can also plug ${y = -4}$ into $\thinspace {-6x+4y = 2}\thinspace$ and get the same answer for $x$ : ${-6x + 4}{(-4)}{= 2}$ ${x = -3}$